Probing fundamental physics with large-scale structure: From galaxy formation to inflation

We show that current surveys of the large-scale structure of the universe have at least as much signal to noise in higher-order statistics as in the power spectrum at weakly nonlinear scales. We discuss how from the measurements of high-order correlation functions of the galaxy number density together with our understanding of dark matter evolution we can place constrain on the relation between the galaxy and the dark matter distributions in terms of the galaxy bias at large scales and by means of the halo model and the halo occupation distribution (HOD) on smaller scales. In particular we show how we can determine the mean of the galaxy HOD using only large-scale information, through galaxy bias parameters determined from the galaxy bispectrum and trispectrum. We also consider possible non-Gaussianity due to quadratic corrections in the primordial gravitational potential parametrized by a non-linear coupling parameter fNL. We study constraints on fNL from measurements of the galaxy bispectrum showing that large-scales redshift surveys can provide results almost as good as cosmic microwave background measurements. For both galaxy bias and HOD determinations and primordial non-Gaussianity constraints we present detailed forecasts for the Sloan Digital Sky Survey.